"its such a stab at my ego to get a ticket the first time I ever broke that darn rule"
Thoughts on how to handle this. First, better planning in advance for where to stop, knowing how crowded popular areas can be in season. Plan accordingly with reasonable back-up sites in mind, even if it means not making as many miles per day as you'd like. Know the trail, know the camp areas in advance and don't over extend yourself such that you arrive at night in a constrained area like this where the risk of not getting a site is so high. Stuff happens. I find that being flexible with my itiniary helps avoid problems like this.
Other than that, if the situation happened as you say, then either 1) calmly try to speak with the ranger and ask their advice on how to handle such issues in the future or 2) quietly and HUMBLELY accept the ticket and then attach a COURTEOUS, NON-COMBATIVE note with your payment explaining the situation regarding the lack of sites, etc. It never helps to get in a shouting match. Be the bigger person. Defuse the situation and you'll have a higher probablity of success at appealing to someone's ie the ranger's sense of fairness, understanding, or whatever.
I wasn't there so i can't really judge what happened wiht the ranger. They have a tough job and i have rarely come accross anybody as you described - not saying it can't happen or didn't happen to you - but most of them want hikers to error on the side of caution when in the wilderness. OTOH, this could be an area where they deal with a lot of scoff-laws.
In any event, as maddening as some situations can be, after you kick a stump, it may help to focus on what you can do in the future - ie what's in your control - to avoid placing yourself in such a predicament again.
Lastly, if none of the above works for you, just have a nice cold beer and congratulate yourself for making a badly needed financial donation to the maintenance of our vauable national parks!